Sunday, December 27, 2009

Fabric of the Cosmos, chapter 4 part 2.

No, I haven't forgotten our book commentary. Here is the next installment of Brian Greene's Fabric of the Cosmos, in which we will try to determine whether modern cosmology can be compatible with Biblical teachings. To catch up, you can read the commentaries to date via links posted in the sidebar under the topic "Fabric of the Cosmos." The first part of chapter four discussed the Heisenberg Uncertainty Principal and related topics. As previously, the excerpts will be in italic and the comments in regular type.

Fabric of the Cosmos
Chapter Four, part 2
Entangling Space
What does it mean to be separate in a quantum universe?
Brian Greene

...Einstein, Uncertainty and a Question of Reality

An important question, and one that may have occurred to you, is whether the uncertainty principle is a statement about what we can know about reality or whether it is a statement about reality itself.

To Bohr, the issue was on par with a Zen koan. Physics addresses only things we can measure. From the standpoint of physics, that IS reality. But in 1935, Einstein together with two colleages, Boris Podolsky and Nathan Rosen, raised this issue.

The intent of the Einstein-Podolsky-Rosen paper was to show that quantum mechanics, while undeniably successful at making predictions and explaining data, could not be the final word regarding the physics of the microcosmos. They wanted to show that every particle does possess a definite position and a definite velocity at any given instant of time, and they they wanted to conclude that the uncertainty principal reveals a fundamental limitation of the quantum mechanical approach.

If every particle has a position and a velocity, but quantum mechanics cannot deal with these features of reality, then quantum mechanics provides only a partial description of the universe. Quantum mechanics, they intended to show, was therefore an incomplete theory of physical reality and, perhaps, merely a stepping-stone toward a deeper framework waiting to be discovered.

Recall, those who grappled with Quantum Physics were reacting against a realization that everything is not etched in stone. Those who stubbornly cling to more Newtonian views of science are doing so because they believe in deterministic theories of reality such as the "watchmaker" and various type of Calvinism that claim everything is known and calculated in advance. However, Uncertainty shows that free will is real, and that God does not micromanage the universe the way many people would like it to be micromanaged.

In fact, the future isn't set in stone until you choose a course of action and follow through on it. Like the structure of an atom, the broad outlines are known (it's properties, as revealed by the prophets) but individuals themselves choose what roles to play - and are hence accountable for their actions. In an atom, the nucleus (representing the past) is fixed and relatively inert, and the shell (the characteristics which determine its properties, are knowable - representing what we know about the future). However, the electrons (representing people, the actors of history) cannot be pinned down. Uncertainty shows that their positions are not fixed until observed (that is, until they make choices about things) and their trajectories cannot be individually known. Thus, they are not set in stone, they are not micromanaged, and this represents free will - and it means the possibility exists that things can go wrong, and that people can and do sin and choose evil.

The deterministic worldview sought to exonerate people from the idea of sin, but quantum physics restores free will and thus personal accountability. And the future, or even the present, is not micromanaged by God. People make choices which have bad outcomes - individually or collectively, with knowledge or in ignorance - and natural processes such as tendency to earthquakes or climate can be affected by human actions or inactions. We are our own worst enemies, yet we tend to blame God for things that go wrong in our lives.

God could have programmed everyone to act perfect, always consider the long-range course of their actions (or their corporation's actions), to always act in the best interests of the community - but that would not be real love, or real faith, or real obedience. It would be programmed - we would be automatons instead of real people, and God didn't want that. So evil happens, primarily because we let it.

Einstein and others who don't like the idea of a "stuff happens" universe try and negate the findings of Quantum Physics - to no avail.

...In actuality, as we will see, they laid the groundwork for demonstrating something even more dramatic: the nonlocality of the quantum world.

Einstein, Podolsky and Rosen invented what appeared to be a convincing and clever end run around ANY source of uncertainty.

For example, if an initial single particle should disintegrate into teo particles of equal mass that fly off "back to back" (like an explosive shooting off two chunks in opposite directions), something that is common in the real of subatomic particle physics, the velocities of the two constituents will be equal and opposite. Moreover, the position of the two constituent particles will also be closely relate, and for simplicity the particles can be thought of as always being equidistant from their common origin.

Einstein, Podolsky and Rosen sought to exploit these relationships to show that each of the particles actually has a definite position and a definite velocity at every given instant of time. EPR reasoned that nothing in your act of measuring the right-moving particle could possibly have any effect on the left-moving particle, because they are separate and distant entities. The left-moving particle is totally oblivious to what you have done or could have done to the right-moving particle. Thus, any feature that you actually learn or could in principal learn about the left-moving particle from studying its right-moving counterpart must be a definite, existing feature of the left-moving particle, totally independent of your measurement.

Thus, EPR concluded that quantum mechanics is an incomplete description of reality. Particles have definite positions and speeds, but the quantum mechanical uncertainty principle shows that these features of reality are beyond the bounds of what the theory can handle.

The Quantum Response

While EPR concluded that each particle has a definite position and velocity at any given moment, notice that if you follow their procedure you will fall short of actually determining these attributes. You could have chosen to measure the right-moving particle's velocity. Had you done so, you would have disturbed its position. On the other hand, had you chosen to measure its position you would have disturbed its velocity. If you don't have both of these attributes of the right-moving particle in had, then you don't have them for the left-moving particle either. There, there is no conflict with the uncertainty principle.

Physics in general, and quantum mechanics in particular, can deal only with the measurable properties of the universe. Anything else is simply not in the domain of physics. If you can't measure both the position and the velocity of a particle, then there is no sense in talking about whether it has both a position and a velocity. [And recall, it has been demonstrated mathematically and experimentally that this is factually so.] Can something be considered real if we can't actually touch it or see it or in some way measure it?

This is the absolute divide between science and religion in microcosm - is anything that can't be measured real? Are the only Real things those that can be measured scientifically?

It is valid for "science" to reject millions of people's personal experiences of prayers answered, unexplainable healings, feeling God's presence or angelic presences, being given tidbits of knowledge or information that they didn't know previously, wildly improbably coincidences, and so forth and so on? Is it valid for those who have had none of these experiences to claim those who did were simply delusional, as British philosopher David Hume and followers of his type of worldview do?

And the flip side should also be considered: should religious people reject science because it seems to differ from the interpretations of their sacred texts that they have been taught? What if those interpretations are obviously not historically or scientifically factual?

Does it have to be either/or, or can science and religion co-exist? My answer would be they can coexist, and in fact do coexist. There is, so far, nothing in quantum physics that contradicts a legitimate interpretation of scripture. Traditions, not so much. But scripture - no problems so far, even in Genesis, as numerous other writers and thinkers have demonstrated. The scripture tells what God did, not how it was done. And time is not fixed, either, as we saw in previous chapters. So science is not an excuse to toss faith out the window. Just because we can't measure something doesn't mean it's not real. Particles are real - we just can't know in advance where they are or where they're going or how fast they're going to get there. Ditto for people and the future.

Bell and Spin

John Bell transformed the central idea of the Eistenstein-Podolsky-Rosen paper from philosophical speculation into a question that could be answered by concrete experimental measurement. Surprisingly, all he needed to accomplish this was to consider a situation in which there were not just two features - for instance, position and velocity - that quantum uncertainty prevents us from simultaneously determining. He showed that if there are three or more features that simultaneously come under the umbrella of uncertainty - three or more features with the property that in measuring one, you contaminate the others and hence can't determine anything about them - then there IS an experiment to address the reality question. The simplest such experiment involves something known as SPIN.

Since the 1920s, physicists have know that particles spin - roughly speaking, they execute rotational motion akin to a soccer ball's spinning around as it heads toward the goal. First, particles - for examples, electrons and photons - can spin only clockwise or counter-clockwise at one never changing rate about any particular axis. A particle's spin can change directions but its rate of spin cannot slow down or speed up. Second, quantum uncertainty applied to spin shows that just as you can't simultaneously determine the position and velocity of a particle, so also you can't determine the spin of a particle about more than one axis.

The mathematics of quantum theory, and decades of experiment, assure us that these characteristics of quantum spin are beyond doubt.

In other worlds, only when you simplify things beyond the point of actual everyday life can you go with a deterministic worldview. Our real life, however, is simply too complex (that is, has so many variables and competing factors) that it defies determinism.

The reason for introducing spin here is not to delve into the intricacies of particle physics. Rather, the example of particle spin will, in just a moment, provide a simple laboratory for extracting wonderfully unexpected answers to the reality question. That is, does a particle simultaneously have a definite amount of spin about each and every axis, although we can never know it for more than one axis at a time because of quantum uncertainty? Or does the uncertainty principle tell us something else?

By studying this question, essentially the same one we asked in the case of particle positions and velocities, we can use spin to probe the nature of quantum relaity (and to extract answers that greatly transcend the specific example of spin).

As explicitly shown by the physicist David Bohm, the reasoning of EPR can easily be extended to the question of whether particles have definite spins about any and all chosen axes. Again, in quantum mechanics the best we can do is predict the probability that the [left-side moving particle as described above] detectors will find clockwise or counterclockwise spin, but we can predict with 100% certainty that whatever one detector finds the other [right-side] will find, too.

Bohm's refinement of the EPR argument is now, for all intents and purposes, the same as it was in the original version that focused on position and velocity. At this stage, seeing no obvious difference from the position/velocity example, you might take Pauli's lead and be tempted to respond that there is no point in thinking about such issues. If you can't actually measure the spin about different axes, what is the point of wondering whether the particles nevertheless has a definite spin - clockwise vs counterclocksise - about each?

Quantum mechanics, and physics more generally, is obliged only to account for features of the world that can be measured. And neither Bohm, Einstein, Podolsky nor Rosen would have argued that the measurements CAN be done. Instead, they argued that the particles possess features forbidden by the uncertainty principle even though we can never explicitly know their particular values. Such features have come to be known as HIDDEN FEATURES, or, more commonly, HIDDEN VARIABLES.

So, E-P-R insist that you have to take it on FAITH that they're actually there, because they cannot be measured. So science has a not small amount of unverifiable presumption going on in there.

Here is where John Bell changed everything. He discovered that even if you can't actually determine the spin of a particle about more than one axis, still, if in fact it has a definite spin about all axes, then there are testable, observable consequences of that spin.

Counting Angels with Angles

IF EPR are correct and each electron actually has a definite spin about all three axes [the classic cartesian coordinate system] - if each electron provides a "program" that definitively determines the result of any of the three possible spin measurements - then we can make the following prediction. Scrutiny of data gathered from many runs of the experiment - runs in which the axis for each detector is randomly and independently selected - will show that more than half the time, the two electron spins agree, both being clockwise or both conterclockwise. If the electron spins do not agree more than half the time, then EPR are wrong.

This is Bell's discovery. It shows that even though you can't actually measure the spin of an electron about more than one axis - even though you can't explicitly "read" the program it is purported to supply to the detector it enters - this does not mean that trying to learn whether it nonetheless has a definite amount of spin about more than one axis is tantamount to counting angels on the head of a pin. Far from it.

Through the Heisenberg Uncertainty Principle, quantum mechanics claims that there are features of the world...that cannot simulataneously have definite values. Instead, particles hover in quantum limbo, in a fuzzy, amorphous probabilistic mixture of all possibilities. Only when measured is one definite outcome selected from the many. Clearly, this is a drastically different picture of reality than that painted by classic physics.

Or by earlier deterministic religious philosophies, such as those espoused by Calvinistic Christian sects and by Rabbinic Authorities that claim everything that happens in the world is pre-determined down to the tiniest detail. But in reality, it simply isn't - our choices, our actions, our inactions, our beliefs are input into a system that is not fixed until we make it so.

Remarkably, John Bell found something that had escaped Einstein, Bohr and all the other giants of 20th century theoretical physics. He found that the mere existence of certain things, even if they are beyond explicit measurements of determination, DOES make a difference - a difference that can be checked experimentally.

Bell had this insight in 1964, but at that time the technology did not exist to undertake the required experiments. By the early 1970s, it did...culminating in the early 1980s with the work of Alain Aspect and collaborators working in France.

When Aspect examined data from a large number of runs of the experiment...he found that the detectors did NOT agree more than 50% of the time. This is an earth-shattering result. Aspect's results show that EPR were proven by experiment - not by theory, not by pondering, not by nature - to be wrong.

But where could they have gone wrong? Well, remember that the EPR argument hangs on one central assumption: if at a given moment you can determine a feature of an object by an experiment done on another, spatially distant object, then the first object must have had this feature all along. [Recall, the experiment involved measuring features of particles that were accelerated one left and one right from a back-to-back starting position, equal opposites.] Their rationale for this assumption was simple and thoroughly reasonable.

In short, the core of the EPR argument is that an object over there does not care about what you do to another object over here.

But recall, we already learned in earlier chapters that in quantum physics, particles that were once connected can stay that way - be linked - even though they have been separated in space and time. The bonds enable one particle to affect the other - so you can say, actually, that one does "care" what happens with the other. They are bound together.

Entangled particles, even though spatially separate, do not operate autonomously.

Recall our earlier observations about the marriage bond between two people, the status of being under the tallit of the head of household, parents to children and vice versa, create bonds of collective responsibility that cannot be easily shaken off. This is why divorce is only permitted for reasons of idolatry or infidelity or other "uncleannesses," and that we are required to make sure our children and elderly parents are reasonably cared for. These bonds make us responsible for the collective welfare of our household, extended family, community, nation, and fellow co-religionists. We are all bound together - and what we do matters to the whole. There is no such thing as a sin that only affects a single person. The ripples spread out.

Similarly, the unclean nature of some things considered food by the goyim, various contaminants, molds and mildews, diseases, forbidden relations and so on and so forth are not things that just affect the person individually. The features of forbidden foods, relationships and various situations which render them "unclean" affect you at the very level of your atoms, and through your quantum connections to your family, friends, and community they affect everyone around you. There are no "islands" in quantum physics. As Dr. Greene continues:

The universe is not local. The outcome of what you do at one place can be linked with what happens at another place, even if nothing travels between the two locations - even if there isn't enough time for anything to complete the journey between the two locations.

This sounds totally bizarre. But there is now overwhelming evidence for this so-called "quantum entanglement." If two photons are entangled, the successful measurement of either proton's spin about one axis "forces" the other, distant photon to have the same spin about the same axis. The act of measuring one photon "compels" the other, possibly distant photon to snap out of the haze of probability and take on a definitive spin value - a value that precisely matches the spin of its distant companion. And that boggles the mind

What should really boggle the mind is that these entanglements were understood by ancient sages long before science ever caught up, making claims based on scripture that are still considered silly superstition by people who don't understand that these issues have basis in the facts of quantum theory. What it boils down to is this: yes, God is smarter than us, and we would be wise to take the teachings of scripture seriously, even if we don't understand how some things affect other things though they appear to be unconnected and we can't understand how they could possibly "hurt" us or anyone else. The fact is, they can. Quantum physics proves it.

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